Time Machine disk is full and can't backup anymore.

Just as an aside. You are probably already aware that it's not a good idea to only rely on a single backup strategy. Especially if your data are critical to you.

For reference, you may find this user tip article I wrote helpful:

• macOS Backup Strategy - Apple Community

Yes, you understand correctly. But that is how it works in theory. In practice, that does not always hold true. One reason is if your TM backups include very large files that change often. For example, VMs (Virtual Machines), created in something like Parallels or VMware. Any time you access them, they change. Since these can be multiple GBs in size, they can quickly use up the destination's storage capacity BEFORE TM has an opportunity to erase older versions.

Hi forgione,

Thank you for using the Apple Support Communities. 

It sounds like your Time Machine disk is getting full and to resolve this problem you would need to follow the recommendations that are found in the Apple resource If the Time Machine backup disk for your Mac is full. 

We hope this helps.

Take care. 

forgione, 

As stated in the Apple support resource If the Time Machine backup disk for your Mac is full, we recommend that you Connect a new backup disk to your Mac or Exclude files from a Time Machine backup on Mac.

Have a good day. 

How much free space do you have on your boot drive?

Is it TM that is full or your internal drive TM needs some space on your internal for snap shots